Sparsity from binary hypothesis testing and application to non-parametric estimation
Dominique Pastor, Abdourrahmane Mahamane Atto · 2008
This paper presents and discusses an alternative notion of sparsity. This notion derives from a theoretical result in bi-nary hypothesis testing and slightly differs from the standard notion of sparsity introduced by Donoho and Johnstone. As an application of this alternative notion of sparsity and as an extension of the detection threshold recently proposed, level-dependent detection thresholds are introduced. The performance of level-dependent detection thresholds is illus-trated in the context of non-parametric estimation by soft thresholding in the wavelet domain. Experimental results show that the resulting approach performs well in compari-son with one of the best up-to-date parametric method. In connection with some results concerning the statistical prop-erties of wavelet coefficients associated with strictly station-ary random processes, prospects are suggested for estimating unknown signals in non-necessarily white or Gaussian noise. 1.